I am rendering in lower resolution, but background is not scaling down to match when rendered
No, blender will not automatically resize the image when you render at 50%. It will only render 50% percent of the pixels around the center of the image (Think of the percentage not as a resize, but as a crop).
If you want to resize use a scale node, set it to render size and Fit, so that the image is rescaled using the output resolution.